Is it possible to move transmission (with all running torrents and downloaded data) from ubuntu GUI onto a transmission-remote server?

I currently have transmission running on a PC running Ubuntu desktop which I leave running continuously. It currently has over a hundred torrents in various levels of activity uploading and downloading. I want to move these onto an Ubuntu Server system running transmission-remote on a more energy efficient former thin wire client machine. I am hoping that transmission stores all the torrent data somewhere and that it is compatible between the GUI version on my Ubuntu desktop and the remote system I intend to set up on my Ubuntu Server system. Can it be done and if so any advice/information very welcome.